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Search for Chiral Magnetic Effects in Au + Au Collisions at STAR Hongwei Ke1, 2 for the STAR Collaboration 1. 2. Mar. 15, 2013 Central China Normal University Brookhaven National Laboratory Moriond QCD and High Energy Interactions 1 Outline Ø Motivation Ø STAR Experiment Ø Observations • Three-particle correlation • Charge asymmetry dependency of pion azimuthal anisotropy Ø Summary Mar. 15, 2013 Moriond QCD and High Energy Interactions 2 QCD Vacuum Transi;on Gluonic field potential energy NC S = 2 -1 instanton 0 1 sphaleron 2 • Gluonic field energy is periodic in Chern–Simons number (NCS) direction • Winding number QW = NCS (+1) NCS ( 1) • Nonzero topological charge generates chirality imbalance NLf NRf = 2QW • QCD vacuum transition è nonzero topological charge è chirality imbalance QW 6= 0 ! µA 6= 0 Mar. 15, 2013 Moriond QCD and High Energy Interactions 3 CME, CSE and CMW • Chiral Magnetic Effect (CME): nonzero axial charge density induces a vector (electric) current along external magnetic field. jV = Nc e µA B 2⇡ 2 è electric charge separation along B field • Chiral Separation Effect (CSE): nonzero vector charge density induces an axial (chiral) current along external magnetic field. Nc e jA = µV B è chiral charge separation The Chiral Magnetic along B fieldWave 2⇡ 2 DK, H.-U. Yee, arXiv:1012.6026 [hep-th] • Chiral Magnetic Wave (CMW): CME and CSE CMEinduce each Chiralother; separation form density waves of electric and chiral charge ✓ @0 ⌥ Nc eB↵ @1 2⇡ 2 ◆ 0 DL @12 jL,R =0 Chiral Propagating chiral wave: Electric collective mode Nuclear Physics A 803, 227 (2008) D. Kharzeev, L. McLerran,Gapless and H. Warringa, 11 D. T. Son and A. R. Zhitnitsky, Phys. Rev. D 70, 074018 (2004) D. Kharzeev and H.-U. Yee, Physical Review D 83, 085007 (2011) Mar. 15, 2013 Moriond QCD and High Energy Interactions 4 Heavy Ion Collisions The existence of the background magnetic field is illustrated in figure 6.2. The p Au + Au sN N = 200GeV Nuclear Physics A 803, 227 (2008). • Chiral symmetry restoration Figure 6.2: A non-central heavy-ion collision showing the magnetic field • Extremely strong magnetic field created in heavy ion collision, ~1015 Tesla! n grid represents the reaction plane. Effect The ovalè orange/red zone represents • Chiral Magnetic out-of-plane electric the charge separation sion participants while the blue partialEffect spheresè represent the spectators. • Chiral Separation out-of-plane chiral The charge separation ctators are highly charged and are moving at speeds close to that of light. • Chiral Magnetic Wave è electric quadrupole moment a mid-central collision with the impact parameter b ∼ .8 times the radius 15, 2013 each blue partial sphere Moriond and High Energy Interactions he GoldMar. nucleus, will QCD contain on average half of 5 Rela;vis;c Heavy-‐Ion Collider Mar. 15, 2013 Moriond QCD and High Energy Interactions 6 STAR detector STAR Experiment BEMC TOF Magnet TPC EEMC BBC upVPD Large & Uniform acceptance for all energies TPC: Full azimuthal angle and large pseudo-rapidity coverage Mar. 15, 2013 Moriond QCD and High Energy Interactions 7 g magnetic field, induces a electric current along the diction of magnetic field. This Chiral Magne;c Effect -plane electric charge separation manifests itself via preferential same-charge par- emission along the diction of magnetic field and opposite-charge particles emission itely along the diction of magnetic field. A P -odd sine term in the Fourier series chargeØ particle azimuthal distribution can be used distribution to describe such e↵ect. Charge particle azimuthal angle • dN↵ ∝1 + 2v1,↵ cos( d + 2a1,↵ sin( ) + 2v2,↵ cos(2 ) + 2a2,↵ sin(2 )+� )+� (4.17) . (4.17), coefficients a reflect the aPα-violating e↵ect, ↵ represent the sign of electric aβ can be • Correlations measured e of particles,• α,= (β =− +,RP-) is azimuthal angle with respect to the reaction plane 52 Ø Three-particle correlation = hcos ( ↵ + • RP )i = [hv1,↵ v1, i + Bin ] [ha↵ a i + Bout ] • Direct flow term v1,α v1,β is small and expected to be the same for SS and OS • In plane (Bin) and out-of-plane (Bout) correlations largely cancel out • aα aβ is sensitive to charge separation os > 0, ↵ = ss < 0, ↵ = S. A. Voloshin, Parity violation in hot qcd: How to detect it, Phys. Rev. C 70, 057901 (2004) Mar. 15, 2013 Moriond QCD and High Energy Interactions 8 20 2.76 TeV Pb+Pb 200 GeV Au+Au -2 62.4 GeV Au+Au 39 GeV Au+Au 27 GeV Au+Au 10 RP ) ] ×104 Centrality dependence of γos & γss Opposite Sign: =0 + Same Sign: = 20 [ = cos( 19.6 GeV Au+Au 11.5 GeV Au+Au 7.7 GeV Au+Au 10 0 STAR preliminary 80 60 40 20 0 60 40 20 % Most Central 0 60 40 20 0 • From 2.76 TeV to 7.7 GeV, changes start to show from the peripheral collisions. ALICE Collaboration, Phys. Rev. Lett. 110, 012301 (2013) Mar. 15, 2013 Moriond QCD and High Energy Interactions 9 Use γos - γss as signal 2.76 TeV Pb+Pb 200 GeV Au+Au 10 62.4 GeV Au+Au 39 GeV Au+Au 27 GeV Au+Au 0 -5 10 19.6 GeV Au+Au 11.5 GeV Au+Au 7.7 GeV Au+Au [ OS - SS ] ×104 5 5 0 -5 80 STAR preliminary 60 40 20 0 60 40 20 % Most Central 0 60 40 20 0 • The signal seems to be disappearing at 7.7 GeV. ALICE Collaboration, Phys. Rev. Lett. 110, 012301 (2013) Mar. 15, 2013 Moriond QCD and High Energy Interactions 10 are likely to mask or reverse this difference in the hadron resonance ‘‘afterburner’’ phase of a heavy ion collision. On the other hand, the smaller difference in the absorption cross sections of negative and positive pions potentially may make it possible to detect the electric quadrupole moment of the plasma through the difference of elliptic flows of pions, v2 ð!þ Þ < v2 ð!" Þ. The effect can be estimated by noting that a strong radial flow aligns the momenta of the emitted hadrons along the direction of the radial flow (see Fig. 3). The asymmetry of the electric charge distribution in the expanding plasma is then translated into the asymmetry in the azimuthal distribution of the positive and negative hadrons: Z Nþ ð"Þ " N" ð"Þ / j0e ðR; "ÞRdR: (8) dN) ¼ N) ½1 þ 2v2 cosð2"Þ' d" * N! ) ½1 þ 2v2 cosð2"Þ + A) r cosð2"Þ': Chiral M agne;c W ave An Electric Quadrupole of QGP B This asymmetry has a 0th Fourier harmonic (monopole) originating from a nonzero net charge density: Z (9) #! e ¼ RdRd"j0e;B¼0 ðR; "Þ: In addition there is a 2nd harmonic (quadrupole) of the form 2qe cosð2"Þ due to the CMW contribution: Z qe ¼ RdRd" cosð2"Þ½j0e ðR; "Þ " j0e;B¼0 ðR; "Þ': (10) e The ratio of the two r ( 2q #! e can be used to parametrize the asymmetry in the azimuthal distributions of positive and negative hadrons: Chiral Separation Effect + - + + (12) In the second line we assume that both v2 and the charge asymmetry A) ( ðN! þ " N! " Þ=ðN! þ þ N! " Þ are small. The elliptic flow therefore becomes charge dependent: v) 2 ¼ v2 + rA) : 2 (13) The magnitude of the effect: Numerical simulation.—As described above, we have computed the evolution of the right and left chiral components of the u and d quarks according to Eq. (3) (at zero rapidity) in a static plasma. For simplicity, we assume the temperature to be uniform within the almond. At the boundary of the plasma, the chiral symmetry is broken and therefore we set v$ ¼ 0. In the transverse (with respect to the magnetic field) direction, we assume a diffusion with a diffusion constant DT estimated [25] as DT ¼ ð2!TÞ"1 within the SakaiSugimoto model. The difference in the elliptic flows of positive and negative pions is given, within our approximation, by Eq. (13). In Fig. 4 we present the ratio r ¼ 2qe =#! e as a function of impact parameter b at different times. In this computation we took the impact parameter dependence of the magnetic field from [3], with the maximal value eBjmax ¼ m2! . To convert this ratio into the difference of the elliptic flows of positive and negative pions according to Eq. (13), we also have to estimate the electric charge asymmetry A) in the quark-gluon plasma that varies between 0 and 1. We do this using the baryon chemical potential and temperature at freeze-out extracted [30] from the data and evaluating the p yields of baryons ffiffi and charged mesons; for the energy of s ¼ 11 GeV we B Chiral Magnetic Effect r 0.01 0.001 + + 10 4 dN± = N± [1 + 2v2 cos(2 )] ± d The QGP acquires a v2 = v2 ⇡ N± [1 + 2v2 cos(2 ) ⌥ Aquadruple ch r cos(2 )] deformation electric r ⌥ Ach 2 + ✓ ◆ vdensity! N to the Chiral qe Magnetic Wave at finitevbaryon due 2 2 = rAch 2 FIG. 3 (color online). Schematic demonstration of the CMWinduced electric quadrupole deformation carried by strong radial flow. 4 6 8 b fm FIG. 4 (color online). The normalized electric quadrupole moment r, eBjmax ¼ m2! , T ¼ 165 MeV. 052303-3 Ach = N+ N+ + N r=2 ⇢¯e What would be theKharzeev, measurable Y. Burnier, D. E. J. Liaoconsequence? and H-U Yee, Phys. Rev. Lett. 107, 052303 (2011) Mar. 15, 2013 Moriond QCD and High Energy Interactions 11 Integrated v2 × 10 STAR Preliminary 0.2 Au + Au 200GeV 30-40% STAR Preliminary 2 Au + Au 200 GeV 30-40% 400 v2(π-) - v (π+) (%) Counts 3 500 300 200 0.1 0 100 0 -0.4 -0.2 0 0.2 0.4 v2{2} (%) observed A ch Au + Au 200 GeV 30-40% 0.15 < p < 0.5 GeV/c T 3.7 3.6 STAR Preliminary -0.1 -0.05 0 0.05 0.1 <observed Ach> Mar. 15, 2013 -0.05 0 0.05 <Ach> π-+ π 3.8 -0.1 Ø v2(π+) and v2(π-) integrated over 0.15 < pT < 0.5 GeV/c Ø v2(π+) and v2(π-) have linear dependency to Ach Ø v2(Ach) slopes of π+ and π- have • opposite sign • similar magnitude Ø v2 difference vs. Ach may have a non-zero intercept Moriond QCD and High Energy Interactions 12 Slope parameter r (%) Slope vs. Centrality 5 STAR Preliminary Au+Au 200 GeV 0.15 < p < 0.5 GeV/c T |η| < 1 0 STAR data UrQMD -5 0 20 CMW (DH) τ = 6 fm/c τ = 5 fm/c τ = 4 fm/c τ = 3 fm/c 40 60 % Most Central • Similar trends between data and theoretical calculations with CMW. • UrQMD cannot reproduce the slopes at √sNN = 200 GeV. Y. Burnier, D. E. Kharzeev, J. Liao, and H.-U. Yee, arXiv:1208.2537 Mar. 15, 2013 Moriond QCD and High Energy Interactions 13 Energy Dependence Slope parameter r (%) 5 5 5 CMW (BS) 0 Au + Au 200GeV STAR Preliminary -5 5 0 20 40 60 0 0 0 -5 Au + Au 62.4 GeV 0.15 < p < 0.5 GeV/c, |η| < 1 -5 T 5 0 20 40 60 0 Au + Au 39 GeV -5 0 20 40 0 20 40 60 0 Au + Au 27 GeV -5 60 5 τ = 3.5 fm/c τ = 3 fm/c τ = 2.5 fm/c τ = 2 fm/c 0 20 40 Au + Au 19.6 GeV -5 60 0 20 40 60 % Most Central • The slope parameter r shows a rise and fall feature from central to peripheral collisions • Slope as a function of centrality shows weak energy dependency • Similar trend to the theoretical calculation based on CMW Mar. 15, 2013 Moriond QCD and High Energy Interactions 14 Summary Ø The three-particle correlation show charge separation with respect to event plane. Signal has similar magnitude from √sNN = 2.76 TeV to 11.5 GeV and seems to disappear at √sNN = 7.7 GeV. Ø The difference between v2(π-) and v2 (π+) shows a linear dependency on charge asymmetry in Au + Au collisions at √sNN = 200, 62.4, 39 and 27 GeV. Ø As a function of collision centrality, the slope parameter r shows a rise and fall feature from central to peripheral collisions and the energy dependence seems weak. The UrQMD model calculations cannot reproduce this feature at √sNN = 200 GeV. Ø Similar trends of slope vs. centrality to the calculations based on CMW. Mar. 15, 2013 Moriond QCD and High Energy Interactions 15